Development of energy consumption optimization model for the electric vehicle routing problem with time windows

Electric vehicles (EVs) are promising transportation tools for supporting green supply chain and cleaner production. In contrast to traditional fossil fuel-powered vehicles, which usually have a short range at lower speeds, EVs have a much longer (even double) range when traveling at lower speeds than high speeds. This feature has a major impact to the vehicle routing problem when EVs are used in the fleet. This study investigated the electric vehicle routing problem with time window (EVRPTW) considering the energy/electricity consumption rate (ECR) per unit of distance traveled by an EV as a function of the speed and load, referred to as EVRPTW-ECR for simplicity. As a consequence, the maximum range of an EV is estimated dynamically according to its speeds and loads along the route. A mixed-integer linear programming (MILP) model was developed for EVRPTW-ECR, where the EV’s speed was treated as a continuous decision variable and the battery capacity, instead of a constant distance, was taken as the range restriction. Two linearization methods, i.e., the inner approximation and outer approximation, were introduced to handle the nonlinear relationship between the traveling speed and travel time with a given parameter ε to control the maximum permissible error. Computational experiments were carried out based on Solomon’s instances to test the efficiency and effectiveness of the proposed model and methods, thereby demonstrating that the MILP model can be solved optimally for up to 25 customers by the CPLEX solver and partially optimized for large instances of up to 100 customers by using a heuristic approach.